On computing the effective multiplication factor using the ADO method

Abstract In this work, the Analytical Discrete Ordinates method, ADO method, is applied to evaluate the effective multiplication factor in criticality problems of a nuclear reactor. To address this class of problems, the multigroup ADO formulation in multislab geometry is here derived taking into account real and complex spectrum. Two approaches are presented to find the desired dominant k-eigenvalue. In the first one, a criticality (characteristic) equation is derived from the complete original equation defined in multiplying media and a combined scheme, using regula-falsi and secant root-finding methods, is used to extract a root of that equation. Such scheme is shown to be very efficient and provided high-quality benchmark results, from lower quadrature order approximations than other schemes available in the literature, as found by the application of the ADO formulation also in several other transport problems. As a second proposed approach, the ADO solution is used along with the usual power iteration method in a simpler procedure. This simpler procedure avoids complex eigenvalues, but it is shown to be less accurate due to required approximations in the source approximation procedure.